1. Copyright 2012 John Wiley & Sons, Inc. Chapter 8 Scheduling

2. A Gantt Chart |||||||||| Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work 0246810 MonthMonth 13579135791357913579

3. 8-3 Standard Abbreviations CPM – Critical Path Method PERT - Program Evaluation and Review Technique

4. 8-4 Background Schedule is the conversion of a project action plan into an operating timetable Basis for monitoring a project One of the major project management tools Work changes daily, so a detailed plan is essential Not all project activities need to be scheduled at the same level of detail

5. 8-5 Background Continued Most of the scheduling is at the WBS level, not the work package level Only the most critical work packages may be shown on the schedule Most of the scheduling is based on network drawings

6. 8-6 Network Scheduling Advantage Consistent framework Shows interdependences Shows when resources are needed Ensures proper communication Determines expected completion date Identifies critical activities

7. 8-7 Network Scheduling Advantage Continued Shows which of the activities can be delayed Determines start dates Shows which task must be coordinated Shows which task can be run parallel Relieves some conflict Allows probabilistic estimates

8. 8-8 Network Scheduling Techniques: PERT (ADM) and CPM (PDM) PERT was developed for the Polaris missile/submarine project in 1958 CPM developed by DuPont during the same time Initially, CPM and PERT were two different approaches – CPM used deterministic time estimates and allowed project crunching – PERT used probabilistic time estimates Microsoft Project (and others) have blended CPM and PERT into one approach

9. 8-9 Terminology Activity - A specific task or set of tasks that are required by the project, use up resources, and take time to complete Event - The result of completing one or more activities Network - The combination of all activities and events that define a project – Drawn left-to-right – Connections represent predecessors

10. 8-10 Terminology Continued Path - A series of connected activities Critical - An activity, event, or path which, if delayed, will delay the completion of the project Critical Path - The path through the project where, if any activity is delayed, the project is delayed – There is always a critical path – There can be more than one critical path

11. 8-11 Terminology Continued Sequential Activities - One activity must be completed before the next one can begin Parallel Activities - The activities can take place at the same time Immediate Predecessor - That activity that must be completed just before a particular activity can begin

12. 8-12 Terminology Continued Activity on Arrow - Arrows represent activities while nodes stand for events Activity on Node - Nodes stand for events and arrows show precedence

13. 8-13 AON and AOA Format Figure 8-3 Figure 8-2

14. 8-14 Constructing the Network Begin with START activity Add activities without precedences as nodes – There will always be one – May be more Add activities that have those activities as precedences Continue

15. 8-15 Solving the Network Table 8-1

16. 8-16 The AON Network from the previous table Figure 8-13

17. Project Network for a House 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house

18. Critical Path A path is a sequence of connected activities running from start to end node in network A path is a sequence of connected activities running from start to end node in network The critical path is the path with the longest duration in the network The critical path is the path with the longest duration in the network Project cannot be completed in less than the time of the critical path Project cannot be completed in less than the time of the critical path

19. The Critical Path A:1-2-3-4-6-7 3 + 2 + 0 + 3 + 1 = 9 months B:1-2-3-4-5-6-7 3 + 2 + 0 + 1 + 1 + 1 = 8 months C:1-2-4-6-7 3 + 1 + 3 + 1 = 8 months D:1-2-4-5-6-7 3 + 1 + 1 + 1 + 1 = 7 months 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house

20. The Critical Path A:1-2-3-4-6-7 3 + 2 + 0 + 3 + 1 = 9 months B:1-2-3-4-5-6-7 3 + 2 + 0 + 1 + 1 + 1 = 8 months C:1-2-4-6-7 3 + 1 + 3 + 1 = 8 months D:1-2-4-5-6-7 3 + 1 + 1 + 1 + 1 = 7 months 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house The Critical Path

21. 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house 12467 3 5 3 20 1 3 11 Start at 3 months Start at 5 months 1 Finish at 9 months Start at 8 months Activity Start Times

22. Early Times ES - earliest time activity can start ES - earliest time activity can start Forward pass starts at beginning of CPM/PERT network to determine ES times Forward pass starts at beginning of CPM/PERT network to determine ES times EF = ES + activity time EF = ES + activity time ES ij = maximum (EF i ) ES ij = maximum (EF i ) EF ij = ES ij - t ij EF ij = ES ij - t ij ES 12 = 0 ES 12 = 0 EF 12 = ES 12 - t 12 = 0 + 3 = 3 months EF 12 = ES 12 - t 12 = 0 + 3 = 3 months 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house

23. Computing Early Times ES 23 = max EF 2 = 3 months ES 23 = max EF 2 = 3 months ES 46 = max EF 4 = max 5,4 = 5 months ES 46 = max EF 4 = max 5,4 = 5 months EF 46 = ES 46 - t 46 = 5 + 3 = 8 months EF 46 = ES 46 - t 46 = 5 + 3 = 8 months EF 67 = 9 months, the project duration EF 67 = 9 months, the project duration 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house

24. Computing Early Times 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house 12467 3 5 3 20 1 3 11 1 (ES = 0, EF = 3) (ES = 5, EF = 8) (ES = 3, EF = 5) (ES = 3, EF = 4) (ES = 5, EF = 6)(ES = 6, EF = 7) (ES = 8, EF = 9) (ES = 5, EF = 5) Early Start and Finish Times

25. Late Times LS - latest time activity can start & not delay project LS - latest time activity can start & not delay project Backward pass starts at end of CPM/PERT network to determine LS times Backward pass starts at end of CPM/PERT network to determine LS times LF = LS + activity time LF = LS + activity time LS ij = LF ij - t ij LS ij = LF ij - t ij LF ij = minimum (LS j ) LF ij = minimum (LS j )

26. Computing Late Times LF 67 = 9 months LF 67 = 9 months LS 67 = LF 67 - t 67 = 9 - 1 = 8 months LS 67 = LF 67 - t 67 = 9 - 1 = 8 months LF 56 = minimum (LS 6 ) = 8 months LF 56 = minimum (LS 6 ) = 8 months LS 56 = LF 56 - t 56 = 8 - 1 = 7 months LS 56 = LF 56 - t 56 = 8 - 1 = 7 months LF 24 = minimum (LS 4 ) = min(5, 6) = 5 months LF 24 = minimum (LS 4 ) = min(5, 6) = 5 months LS 24 = LF 24 - t 24 = 5 - 1 = 4 months LS 24 = LF 24 - t 24 = 5 - 1 = 4 months 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house

27. Computing Late Times LF 67 = 9 months LF 67 = 9 months LS 67 = LF 67 - t 67 = 9 - 1 = 8 months LS 67 = LF 67 - t 67 = 9 - 1 = 8 months LF 56 = minimum (LS 6 ) = 8 months LF 56 = minimum (LS 6 ) = 8 months LS 56 = LF 56 - t 56 = 8 - 1 = 7 months LS 56 = LF 56 - t 56 = 8 - 1 = 7 months LF 24 = minimum (LS 4 ) = min(5, 6) = 5 months LF 24 = minimum (LS 4 ) = min(5, 6) = 5 months LS 24 = LF 24 - t 24 = 5 - 1 = 4 months LS 24 = LF 24 - t 24 = 5 - 1 = 4 months 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house 12467 3 5 3 20 1 3 11 1 ES = 3, EF = 5 LS = 3, LF = 5 ( ) ES = 5, EF = 8 LS = 5, LF = 8 ( ) ES = 3, EF = 4 LS = 4, LF = 5 ( ) ES = 0, EF = 3 LS = 0, LF = 3 ( ) ES = 5, EF = 5 LS = 5, LF = 5 ( ) ES = 5, EF = 6 LS = 6, LF = 7 ( ) ES = 8, EF = 9 LS = 8, LF = 9 ( ) ES = 6, EF = 7 LS =7, LF = 8 ( ) Early and Late Start and Finish Times

28. Activity Slack Activities on critical path have ES = LS & EF = LF Activities on critical path have ES = LS & EF = LF Activities not on critical path have slack Activities not on critical path have slack S ij = LS ij - ES ij S ij = LS ij - ES ij S ij = LF ij - EF ij S ij = LF ij - EF ij S 24 = LS 24 - ES 24 = 4 - 3 = 1 month S 24 = LS 24 - ES 24 = 4 - 3 = 1 month

29. Activity Slack Data 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house ActivityLSESLFEFSlacks *1-200330 *2-333550 2-443541 *3-455550 4-565761 *4-655880 5-676871 *6-788990 * Critical path

30. Activity Slack Data 3 20 1 3 11 1 12467 3 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house ActivityLSESLFEFSlacks *1-200330 *2-333550 2-443541 *3-455550 4-565761 *4-655880 5-676871 *6-788990 * Critical path 12467 3 5 3 20 1 3 11 1 Activity Slack S = 0 S = 1 S = 0

31. 8-31 Total Slack vs. Free Slack Slack calculations shown up to this point are for “Total Slack” Total Slack is the most a task can be delayed with changing the plan for project completion. – May cause delay on a successor, eating into its slack time. Free Slack is the amount a task can be delayed with no affect on any other task.

32. Probabilistic Time Estimates Reflect uncertainty of activity times Reflect uncertainty of activity times Beta distribution is used in PERT Beta distribution is used in PERT

33. Probabilistic Time Estimates Reflect uncertainty of activity times Reflect uncertainty of activity times Beta distribution is used in PERT Beta distribution is used in PERT a = optimistic estimate m = most likely time estimate b = pessimistic time estimate where Mean (expected time): t = a + 4 m + b 6 Variance:  2 = b - a 6 2

34. Example Beta Distributions P(time) Time amtbamtb m = t Time Time ba Figure 6.11

35. Southern Textile Company System changeover 2 4 6 17359 8 Manual Testing Dummy System Training Dummy System Testing Orientation Position recruiting System development Equipment installation Equipment testing and modification Final debugging Job training A B CED F G H I JK L M

36. Activity Estimates 1 - 2A6810 1 - 3B369 1 - 4C135 2 - 5D000 2 - 6 E2412 3 - 5 F234 4 - 5G345 4 - 8H222 5 - 7I3711 5 - 8J246 8 - 7K000 6 - 9L147 7 - 9M11013 TIME ESTIMATES (WKS) ACTIVITY amb 2 4 6 17359 8

37. Activity Estimates 1 - 2681080.44 1 - 336961.00 1 - 413530.44 2 - 500000.00 2 - 6 241252.78 3 - 5 23430.11 4 - 534540.11 4 - 822220.00 5 - 7371171.78 5 - 824640.44 8 - 700000.00 6 - 914741.00 7 - 91101394.00 TIME ESTIMATES (WKS)MEAN TIMEVARIANCE ACTIVITY ambt  2 2 4 6 17359 8

38. 2 4 6 17359 8 Early and Late Times For Activity 1-2 a = 6, m = 8, b = 10 t = = = 8 weeks a + 4 m + b 6 6 + 4(8) + 10 6  2 = = = week b - a 6 2 10 - 6 6249

39. 2 4 6 17359 8 Early and Late Times ACTIVITY t   ESEFLSLFS 1 - 280.4408191 1 - 361.0006060 1 - 430.4403252 2 - 500.0088991 2 - 6 52.7881316218 3 - 5 30.1169690 4 - 540.1137592 4 - 820.0035141611 5 - 771.789169160 5 - 840.4491312163 8 - 700.00131316163 6 - 941.00131721258 7 - 994.00162516250

40. Southern Textile Company 2 4 6 17359 8 ES = 9, EF = 16 LS = 9, LF = 16 ES = 0, EF = 8 LS = 1, LF = 9 ES = 0, EF = 6 LS = 0, LF = 6 ES = 6, EF = 9 LS = 6, LF = 9 ES = 0, EF = 3 LS = 2, LF = 5 ES = 3, EF = 7 LS = 5, LF = 9 ES = 9, EF = 13 LS = 12, LF = 16 ES = 8, EF = 8 LS = 9, LF = 9 ES = 13, EF = 13 LS = 16, LF = 16 ES = 3, EF = 5 LS = 14, LF = 16 ES = 16, EF = 25 LS = 16, LF = 25 ES = 13, EF = 17 LS = 21, LF = 25 ES = 8, EF = 13 LS = 16, LF = 21 8 5 4 637 9 3 2 40 0

41. Southern Textile Company 2 4 6 17359 8 ES = 9, EF = 16 LS = 9, LF = 16 ES = 0, EF = 8 LS = 1, LF = 9 ES = 0, EF = 6 LS = 0, LF = 6 ES = 6, EF = 9 LS = 6, LF = 9 ES = 0, EF = 3 LS = 2, LF = 5 ES = 3, EF = 7 LS = 5, LF = 9 ES = 9, EF = 13 LS = 12, LF = 16 ES = 8, EF = 8 LS = 9, LF = 9 ES = 13, EF = 13 LS = 16, LF = 16 ES = 3, EF = 5 LS = 14, LF = 16 ES = 16, EF = 25 LS = 21, LF = 25 ES = 13, EF = 17 LS = 21, LF = 25 ES = 8, EF = 13 LS = 16, LF = 21 8 5 4 637 9 3 2 40 0  2 =  2 +  2 +  2 +  2 = 1.00 + 0.11 + 1.78 + 4.00 = 6.89 weeks^2 13355779 Total project variance

42. Probabilistic Network Analysis Determine probability that project is completed within specified time where  = t p = project mean time  =project standard deviation x =proposed project time Z =number of standard deviations x is from mean Z =Z =Z =Z = x -  

43. Normal Distribution Of Project Time  = t p Timex ZZProbability

44. Southern Textile Example What is the probability that the project is completed within 30 weeks?

45. Southern Textile Example What is the probability that the project is completed within 30 weeks?  = 25 Time (weeks) x = 30 P( x  25 weeks)

46. Southern Textile Example What is the probability that the project is completed within 30 weeks?  = 25 Time (weeks) x = 30 P( x  25 weeks)  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = 1.91 x -   30 - 25 2.62

47. Southern Textile Example What is the probability that the project is completed within 30 weeks?  = 25 Time (weeks) x = 30 P( x  25 weeks)  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = 1.91 x -   30 - 25 2.62 From Excel, a Z score of 1.91 corresponds to a probability = normsdist(1.91) = 0.9719

48. Southern Textile Example What is the probability that the project is completed within 22 weeks?  = 25 Time (weeks) x = 22 P( x  22 weeks) 0.3729

49. Southern Textile Example What is the probability that the project is completed within 22 weeks?  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = -1.14 x -   22 - 25 2.62  = 25 Time (weeks) x = 22 P( x  22 weeks) 0.3729

50. Southern Textile Example What is the probability that the project is completed within 22 weeks?  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = -1.14 x -   22 - 25 2.62 From Excel, a Z score of -1.14 corresponds to a probability = normsdist(-1.14) = 0.1271  = 25 Time (weeks) x = 22 P( x  22 weeks) 0.3729

51. Normal Distribution Of Project Time When doing these problems in Excel use: norm.dist() to find a probability norm.inv() to find a date.

52. 8-52 Calculating Activity Times

53. 8-53 Uncertainty of Project Completion Time Assume activities are statistically independent Variance of a set of activities is the sum of the individual variances Interested in variances along the critical path

54. 8-54 Toward Realistic Time Estimates Calculations are based on 1% chance of beating estimates Calculations can also be based on 5% or 10% Changing the percentage requires changing the formulae for variance When using 5%, the divisor changes to 3.29 When using 10%, the divisor changes to 2.56

55. 8-55 Precedence Diagramming Finish to start Start to start Finish to finish Start to finish

56. Four Types of Dependencies – FS (Finish-to-Start) When A Finishes, B can Start Example: Foundation must be finished before framing starts PDM AON

57. Four Types of Dependencies – FF (Finish-to-Finish) When A Finishes, B can Finish Example: testing of an application cannot finish until coding is finished PDM AON

58. Four Types of Dependencies – SS (Start-to-Start) When A Starts, B can Start Example: Data entry can start as soon as data collection starts PDM AON

59. Four Types of Dependencies – SF (Start-to-Finish) When A Starts, B can Finish Example: legacy system cannot be shut down (finished) until new system has gone online (started) PDM AON

60. Three categories of dependencies – Mandatory Inherent (physical limitations) – Discretionary Preferred (defined by team) – External Legal (government) Contractual Other Dependency Determination

61. Lead – Successor can start before activity finishes – Example: Landscaping can begin before the completion of the building Shown on the diagram as a finish-to-start relationship with a lead Lead = (-1)Lag in MSP Applying Leads and Lags

62. Lag – Delay between activities Example: Concrete must cure before next activity can begin Shown on the diagram as a start-to-start relationship with a lag Applying Leads and Lags 15 d

63. Work (or Effort) is the number of workdays or work hours required to complete a task Duration includes the actual amount of time worked on an activity and the elapsed time Work = Duration x Units Estimating Activity Durations

64. Effort Driven = Constant Work 8-64 Task TypeEffort Driven ONEffort Driven OFF Fixed UnitsAdding Resources shortens duration Adding Resources increases total work, but not units and duration Fixed DurationAdding Resources decreases units for each resource Adding Resources increases total work, but not units and duration Fixed WorkAdding Resources shortens duration (N/A)